$3\mathrm{.}5$ Modify and submit the program Sum of Integers given in section $3\mathrm{.}16$ to use the formula:

#

# Sum $=($N$*($N$+1))/2$

# addi,shift

# Since either N or N$+1$ will be even, the product is even, and thus be divisible by two.

# Since the product is positive you can use a shift to perform the division.

# Test your program on the MIPS simulator. What is the upper bound on N for the program

# to give a correct answer? How large does N need to be for you to detect an observable

# delay in the original program?